I can't tell, Trekker47, if you are Irish or Irish-American or Irish-something else, so forgive me if I tell you things about the U.S. that you might already know. The reason Trek -- and other shows, for that example -- felt free to use Irish stereotypes is because nobody seriously believes them any more. Yes, I know all about the bad old days of "No Irish Need Apply," but those days are long gone and were long gone before I was born. And the reason is that it's kind of difficult to be racist about a group to which one belongs. I don't know what percentage of U.S. citizens (of western European blood, anyway) have at least some Irish in their ancestry, but the answer would be "a really high percentage." I am included in that group, by the way, and I'd bet big money that if you looked up the various persons connected to TNG, you would find lots of them in that group as well. Irish ancestry is everywhere.
So there is no general prejudice against the Irish in the U.S. Really. None. We even have a very famous college that uses a similar stereotype -- the University of Notre Dame's Fighting Irish. It's a Catholic university, attended over the years by many Irish Catholics (as well as other kinds of Catholics and non-Catholics), and all I can say is that if they perceive their mascot's name as offensive, they don't appear to be in any hurry to change it since the university was founded in 1842.
In contrast, many other forms of racism are not gone, much less long gone, which is why, for example, just about the only folks outside the KKK who can safely use black- or Hispanic-oriented stereotypes to a general audience and get away with it are black or Hispanic people. (Apparently Speedy Gonzales cartoons are now non-PC but the Mexican guys that my husband works with think they are hilarious -- they quote Speedy and everything.)
So that's why Irish stereotypes are used. They are safe, and the reason they are safe is because they are not about some downtrodden minority and because they have no connection to reality and everybody knows it. I don't know one single person who would watch that episode and say or think, "Yes, the Irish really are just like that." It's exactly, and I do mean exactly, like portraying all British as drinking tea all the time and saying "Pip pip!" or portraying all French males as wearing berets and chasing females a la Pepe le Peau.
Mind you, I'm not saying these quick-and-easy stereotypes are a great idea, particularly not for a show that wants to be taken seriously (which Pepe le Peau does not, of course). They are a lazy writer's way of saving himself the effort of doing original thinking and writing, of coming up with a more subtle way of conveying the idea of, "Hey! Let's make it so that a bunch of high-tech, uptight clones are forced to interact with a a primative, earthy race! Won't THAT be a hoot?" The episode could definitely have been much better. Why not just do exactly the same thing, sans the Irish accents, for example? Lots of societies besides the Irish wore homespun, kept pigs and drank liquor, after all. But I am confident, Trekker47, that what you sense as prejudice is just...sloppy, lazy writing. If you want to go around looking for anti-Irish sentiment among the writers and so on, that's your right, but I think you will be upsetting yourself for no good reason. Be annoyed at the foolish premise, by all means, but not by some TNG-fostered sentiment "against" Irish people.